There are no buses to Sykeside in the winter. The closest you can get is Patterdale, but then you'd have to get the train to Penrith to link with that bus, and you'd have to stay overnight in Penrith and get the bus the following morning.
The taxi option might be best. Taxis park opposite the railway station at Windermere, and Kirkstone Pass would be the closest, easily accessible spot for a wild camp. Pretty awful place to be if the weather is bad though... in which case talk to the pub folk about B&B!
Edited to add...
If you do set your heart on Sykeside, and it's likely that Kirkstone will be snow-bound, or you think you might not be able to find a taxi driver brave enough to cross it... then stay on the train to Penrith and get a taxi from the station to Patterdale and Sykeside. (The last bs from Penrith to Patterdale is at 1600, so that's no use to you.)
Edited: 04/02/2012 at 20:52